一类减算子不动点定理的推广及应用

The Generalization and Application of Fixed Point Theory about some Decreasing Operator

利用锥理论,单调迭代技巧以及谱半径的相关知识研究了一类非紧非连续减算子的不动点的存在、唯一性及迭代收敛,获得了新的结果。作为其应用重点讨论了非减算子方程解的存在唯一性,并给出了迭代序列收敛于解的误差估计,改进和推广了某些已知结果。

By using the theory of cone, monotone iteratived techniques and the knowledge about spectral radius,the existence, uniqueness and iteration of some noncompact and noncontinuous decreasing operator＇ fixed point are discussed, and new conclusions are gained. For its application, the existence and uniqueness of solutions of non - decreasing operator equations are studied, and the iteration sequences which converge to solution of operator equations and the error estimates are also given. The results presented here improve and generalize some corresponding results.